Yes, there is a solenoid on the starter motor and it usually clicks if the battery is very low on power - enough to energize the solenoid but not enough to turn the engine over. Batteries struggle when it is as cold as this , particularly if you haven't used it for a day or two. If the battery is more than three years old it's probably had it - but if you can charge it up (or get a jump start and go drive for 20 minutes) it may recover sufficiently.
Richard
January 2009
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